let G1 be _Graph; :: thesis: for G2 being G1 -isomorphic _Graph
for G3 being SimpleGraph of G1
for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic
let G2 be G1 -isomorphic _Graph; :: thesis: for G3 being SimpleGraph of G1
for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic
let G3 be SimpleGraph of G1; :: thesis: for G4 being SimpleGraph of G2 holds G4 is G3 -isomorphic
let G4 be SimpleGraph of G2; :: thesis: G4 is G3 -isomorphic
set G5 = the removeLoops of G1;
set G6 = the removeLoops of G2;
A1: the removeLoops of G2 is the removeLoops of G1 -isomorphic by Th166;
( G3 is removeParallelEdges of the removeLoops of G1 & G4 is removeParallelEdges of the removeLoops of G2 ) by GLIB_009:121;
hence G4 is G3 -isomorphic by A1, Th168; :: thesis: verum